p=\frac{2}{\left(1+\frac{1}{2\sqrt{q+\frac{1}{4}}}\right)\left(\frac{1}{2}+\sqrt{q+\frac{1}{4}}\right)^8+\left(1-\frac{1}{2\sqrt{q+\frac{1}{4}}}\right)\left(\frac{1}{2}-\sqrt{q+\frac{1}{4}}\right)^8}\cdot 500=56.6213